The present invention relates to a three-dimensional tracer control system which permits a highly accurate machining operation.
There has heretofore been put to practical use a three-dimensional tracer control system that traces the configuration of a model in the X-Y plane by X- and Y-axis direction displacement signals available from a tracer head and controls the trace velocity in the Z-axis direction by a Z-axis direction displacemnt signal. FIG. 1 illustrates in block form an example of such a conventional system. In FIG. 1, reference numeral 1 indicates a tracer head; 2 designates a stylus; 3 identifies a displacement resultant circuit; 4 and 9 denote adders; 5 and 6 represent velocity components arithmetic circuits; 7 shows a distributing circuit; 8 refers to a displacement direction index circuit; 10 indicates an amplifier; 11 to 13 designate drivers; and 14 to 16 identify motors.
The tracer head 1 yields displacement signals .epsilon..sub.x, .epsilon..sub.y and .epsilon..sub.z corresponding to displacement of the stylus 2 in the X- , Y- and Z-axis directions. The displacement signals .epsilon..sub.x and .epsilon..sub.y are provided to the displacement resultant circuit 3 and the displacement direction index circuit 8 and the displacement signal .epsilon..sub.z is applied to the adder 9. The displacement resultant circuit 3 obtains a resultant displacement signal .epsilon.=.sqroot..epsilon..sub.x.sup.2 +.epsilon..sub.y.sup.2 from the displacement signals .epsilon..sub.x and .epsilon..sub.y and applies it to the adder 4. The displacement direction index circuit 8 derives displacement direction signals sin .theta. and cos .theta. from the displacement signals .epsilon..sub.x and .epsilon..sub.y and provides them to the distributing circuit 7.
The adder 4 detects a difference .DELTA..epsilon.=.epsilon.-.epsilon..sub.0 between the resultant displacement signal .epsilon. from the displacement resultant circuit 3 and a reference displacement signal .epsilon..sub.0. The velocity components arithmetic circuits 5 and 6, which are supplied with the output from the adder 4, derive therefrom a normal-direction velocity signal V.sub.N and a tangential-direction velocity signal V.sub.T, respectively, which are provided to the distributing circuit 7. Based on the normal-direction velocity signal V.sub.N, the tangential-direction velocity signal V.sub.T and the displacement direction signals sin .theta. and cos .theta., the distributing circuit 7 produces velocity command signals in the X- and Y-axis directions by which the difference .DELTA..epsilon. between the resultant displacement signal .epsilon. and the reference displacement signal .epsilon..sub.0 is reduced to zero. The velocity command signals are applied to the drivers 11 and 12, which drive the motors 14 and 15 in response to the velocity command signals.
The adder 9, which is supplied with the displacement signal .epsilon..sub.z, detects a difference .epsilon..sub.z -.epsilon..sub.z0 between it and a reference displacement signal .epsilon..sub.z0. The difference .epsilon..sub.z -.epsilon..sub.z0 thus obtained is applied via the amplifier 10 to the driver 13, causing it to drive the motor 16 which performs the Z-axis control. By driving the motors 14 to 16 in the manner described above, the tracer head 1 and a cutter (not shown) are fed together to achieve machining operations of a work (not shown).
Now, consider tracing of such a slope as shown in FIG. 3 which has an angle of inclination .alpha.. In this case, assuming that the trace velocity in the X-Y plane is V.sub.XY, it is necessary that the trace velocity V.sub.Z in the Z-axis direction be as follows: EQU V.sub.Z =V.sub.XY .multidot.tan .alpha. (1)
In the conventional three-dimensional tracer control system, since the trace velocity V.sub.Z in the Z-axis direction is in proportion to the difference (.epsilon..sub.z -.epsilon..sub.z0) between the displacement signal .epsilon..sub.z and the reference displacement signal .epsilon..sub.z0 in the Z-axis direction, the Z-axis velocity V.sub.Z is given by the following expression (2): EQU V.sub.Z =K(.epsilon..sub.z -.epsilon..sub.z0) (2)
where K is a proportional constant.
From expressions (1) and (2), the displacement signal .epsilon..sub.z in the Z-axis direction becomes as follows: ##EQU1##
As is evident from expression (3), the displacement signal .epsilon..sub.z in the Z-axis direction varies with a change in the feed rate V.sub.XY in the X-Y plane or the angle of inclination .alpha., resulting in variations in machining accuracy. In other words, the prior art tracer control system has the defects of inaccurate machining operations and degraded traceability in the X-Y plane.